Writing is an important part of my thought process. We are encouraged to go to the temple to seek out answers, and I was wondering why I never see people write down their impressions in the Celestial Room. Is it not allowed to bring a pen and paper into the celestial room?
You are a questioner after my own heart! As a matter of habit I usually keep a pen and writing pad with me wherever I go. When I go to the temple, I leave the pen and pad in my locker after changing into my temple clothing. Certainly it would be helpful to be able to write down impressions as they come in the Celestial Room; but I have always assumed that the practice would be discouraged because of–for example–concerns over keeping the temple ceremony confidential, or simply avoiding creating distractions for other temple patrons. This might be a good question for you to take to a member of your local temple presidency for further explanation.
I would gently suggest, however, that the meditative experience we associate with temple worship doesn’t need to end once we walk out of the Celestial Room. If I can continue that pondering process even as I return to the locker room and prepare to leave the temple, my experience is that the things I have learned will linger long enough for me to get my trusty pad and pen, sit down in the foyer for a few moments, and commit those new insights to paper before leaving the building.